1 /* 2 * Single-precision vector cos function. 3 * 4 * Copyright (c) 2019-2023, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "mathlib.h" 9 #include "v_math.h" 10 11 static const struct data 12 { 13 float32x4_t poly[4]; 14 float32x4_t range_val, inv_pi, half_pi, shift, pi_1, pi_2, pi_3; 15 } data = { 16 /* 1.886 ulp error. */ 17 .poly = { V4 (-0x1.555548p-3f), V4 (0x1.110df4p-7f), V4 (-0x1.9f42eap-13f), 18 V4 (0x1.5b2e76p-19f) }, 19 20 .pi_1 = V4 (0x1.921fb6p+1f), 21 .pi_2 = V4 (-0x1.777a5cp-24f), 22 .pi_3 = V4 (-0x1.ee59dap-49f), 23 24 .inv_pi = V4 (0x1.45f306p-2f), 25 .shift = V4 (0x1.8p+23f), 26 .half_pi = V4 (0x1.921fb6p0f), 27 .range_val = V4 (0x1p20f) 28 }; 29 30 #define C(i) d->poly[i] 31 32 static float32x4_t VPCS_ATTR NOINLINE 33 special_case (float32x4_t x, float32x4_t y, uint32x4_t odd, uint32x4_t cmp) 34 { 35 /* Fall back to scalar code. */ 36 y = vreinterpretq_f32_u32 (veorq_u32 (vreinterpretq_u32_f32 (y), odd)); 37 return v_call_f32 (cosf, x, y, cmp); 38 } 39 40 float32x4_t VPCS_ATTR V_NAME_F1 (cos) (float32x4_t x) 41 { 42 const struct data *d = ptr_barrier (&data); 43 float32x4_t n, r, r2, r3, y; 44 uint32x4_t odd, cmp; 45 46 #if WANT_SIMD_EXCEPT 47 r = vabsq_f32 (x); 48 cmp = vcgeq_u32 (vreinterpretq_u32_f32 (r), 49 vreinterpretq_u32_f32 (d->range_val)); 50 if (unlikely (v_any_u32 (cmp))) 51 /* If fenv exceptions are to be triggered correctly, set any special lanes 52 to 1 (which is neutral w.r.t. fenv). These lanes will be fixed by 53 special-case handler later. */ 54 r = vbslq_f32 (cmp, v_f32 (1.0f), r); 55 #else 56 cmp = vcageq_f32 (x, d->range_val); 57 r = x; 58 #endif 59 60 /* n = rint((|x|+pi/2)/pi) - 0.5. */ 61 n = vfmaq_f32 (d->shift, d->inv_pi, vaddq_f32 (r, d->half_pi)); 62 odd = vshlq_n_u32 (vreinterpretq_u32_f32 (n), 31); 63 n = vsubq_f32 (n, d->shift); 64 n = vsubq_f32 (n, v_f32 (0.5f)); 65 66 /* r = |x| - n*pi (range reduction into -pi/2 .. pi/2). */ 67 r = vfmsq_f32 (r, d->pi_1, n); 68 r = vfmsq_f32 (r, d->pi_2, n); 69 r = vfmsq_f32 (r, d->pi_3, n); 70 71 /* y = sin(r). */ 72 r2 = vmulq_f32 (r, r); 73 r3 = vmulq_f32 (r2, r); 74 y = vfmaq_f32 (C (2), C (3), r2); 75 y = vfmaq_f32 (C (1), y, r2); 76 y = vfmaq_f32 (C (0), y, r2); 77 y = vfmaq_f32 (r, y, r3); 78 79 if (unlikely (v_any_u32 (cmp))) 80 return special_case (x, y, odd, cmp); 81 return vreinterpretq_f32_u32 (veorq_u32 (vreinterpretq_u32_f32 (y), odd)); 82 } 83